i cant seem to figure this out

What is m^3 – 3m^2 = 5m – 15 factored?

It's interesting that the problem was posed this way because you might notice that you can use the Distributive Property on both sides:

m^2(m – 3) = 5(m – 3)

At this point you might decide to say "If m ≠ 3 then I can divide both sides by (m–3) to get m^2 = 5, where m = ±√(5) are the only two answers."

However, if instead you subtracted 5(m – 3) from both sides:

m^2(m – 3) – 5(m – 3) = 0

and used the Distributive Property:

(m – 3)(m^2 – 5) = 0

Substitute (√(5))^2 for 5:

(m – 3)(m^2 – (√(5))^2) = 0

Use Difference of Squares:

(m – 3)(m + √(5))(m – √(5)) = 0

That's the answer to, "What is m^3 – 3m^2 = 5m – 15 factored?"

But now, using the Zero Product Property, you can find the values of m that make it true:

(m – 3) = 0 ==> m = 3

(m – √(5)) = 0 ==> m = + √(5)

(m + √(5)) = 0 ==> m = – √(5)